Method For Spatial Variables Research Articles

Modeling and numerical simulation of dissolved oxygen and biochemical oxygen demand concentrations with Holling type III kinetic relationships

Mathematical models have been widely used for the study of water quality. Regarding the pollution of water resources by organic matter, dissolved oxygen (DO) and biochemical oxygen demand (BOD) are important indicators for their monitoring. In this way, this research presents a two-dimensional mathematical model in space that evolves over time, for the study of the variations in concentrations of these variables, through a coupled system of non-linear partial differential equations, with Holling type III reaction kinetics between DO and BOD. Under some simplifications, the stability of the equilibrium points of the model is analyzed. An approximate solution is proposed using the centered finite difference (CFD) method for spatial variables and the Crank–Nicolson method for the temporal variable. An upwind scheme was employed in the advective-term discretization. Computer simulations were performed using Matlab software, in a rectangular domain. For the advective transport, the influences of the wind and the current given by a parabolic profile were considered. We performed a series of space-time numerical simulations and found that the model allows the analysis of regions with higher and/or lower DO and BOD concentrations, as well as the temporal variations of concentrations at specific points in the domain, and the influence of diffusive-advective transport in the mass transfer process.

Comparing causal techniques for rainfall variability analysis using causality algorithms in Iran

Causal analysis (CA) is a strong quantitative approach whose mechanisms have climatic predictions. In this study, we studied the patterns of causality (PC) on the effect of rainfall (ER) using climatic series collected from 170 stations for the period 1975–2014 in Iran. Next, we predicted the causal relationships of climatic variables using causal models, including first-generation techniques (FGT), second-generation techniques (SGT), third-generation techniques (TGT), and causal hybrid techniques (CHT). Then, we estimated the causal models using partial squares algorithms (PSA), mechanical equations modeling algorithms (MEMA) such as exploratory and confirmatory methods, and spatial variability methods such as geostatistics and spatial statistical methods. Finally, we evaluated the quality of the methods using the goodness of fit indices, including absolute fit indices (AFI), comparative fit indices (CFI), and parsimonious fit indices (PFI). The results showed that CHT algorithm more suitably predicted the climatic spatiotemporal effect variability (SEV) by extracting direct, indirect, and total effects of climatic variables. Based on the CHT algorithm, the highest and lowest effect values were observed in total effects of winter rainfall (0.98) and summer rainfall variables (0.1), respectively. The SEV ranged from 0.8 to 0.98 for the winter rainfall total effects of CHT in Iran. Using CHT, most of the predicted SEV, particularly the rainfall series, displayed SEV varying from 80% to 98% of the winter rainfall total effects to the annual rainfall in Iran. Similarly, based on the CHT, the highest and lowest SEV values were in western, eastern, and southern regions and in central regions, respectively. In addition, the SEV varied within the range of 0.6–0.74 (varying from 60% to 74% for the autumn rainfall total effects of the annual rainfall in Iran) for the autumn rainfall total effects in Iran. Finally, the SEV of this type of analytical pattern as well as designated subject of CA applications in the atmospheric science and environmental science are discussed.